The World’s Oldest Mathematical Artifacts
What do you know about the Ishango bone? It’s a mathematical artifact found in the Congo. Dating back to about 20,000 years ago, this bone is carved with simple notches that symbolize mathematical and astronomical notations that scientists are still attempting to understand. And there are others like it.
Examples include the Thaïs Bone (12,000 years old, France), the Abri Blanchard Bone (27-34,000 years old, France), the Wolf Bone (30,000 years old, Czech Republic), and the Lebombo Bone (35,000 years old, Southern Africa). They’re all super-old, 100% Black-owned, highly mathematical, and worthy of your research. But I’ll make it easy. The following is an excerpt from The Science of Self, Volume One, dealing with this subject. On the house.
Mathematical Systems for Divination
In the Ishango region of Zaïre (now called Congo) near Lake Edward, archaeologists discovered a bone tool engraved with notches and a sharp piece of quartz affixed to one end, perhaps for further engraving or writing. The three rows of notches led scientists to assume at first that it was a tally stick, but others have suggested that the groupings of notches indicate a mathematical understanding that goes beyond counting. The Ishango bone tool is at least 20,000 years old.[i] On the tool are three rows of notches demonstrating some of the mathematical knowledge among the people of this region.
Jean de Heinzelin, professor emeritus of Ghent University and an authority in African archeology, compared prehistoric Ishango harpoon heads to those found in northern Sudan and ancient Egypt and proposed a link between Ishango mathematics and the origins of ancient Egyptian mathematical knowledge. Regarding the Ishango bone, de Heinzelin reported:
It is possible to trace the influence of the Ishango technique on other African peoples by examining harpoon points at other sites. From central Africa the style seems to have spread northward. At Khartoum near the upper Nile there is a site that was occupied considerably later than Ishango. The harpoon points found there show a diversity of styles. Some have the notches that seem to have been invented first at Ishango. Near Khartoum, at Es Shanheinab, is a Neolithic site that contains harpoon points bearing the imprint of Ishango ancestry. From there the Ishango technique moved westward, but a secondary branch went northward from Khartoum along the Nile Valley to Nagada in Egypt…The first example of a well worked out mathematical table dates from the dynastic period in Egypt. There are some clues, however, that suggest the existence of cruder systems in predynastic times. Because the Egyptian number system was a basis and a prerequisite of classical Greece, and thus for many of the developments in science that followed, it is even possible that the modern world owes one of its greatest debts to the people who lived at Ishango. Whether or not this is the case, it is remarkable that the oldest clue to the use of a number system by man dates back to central Africa of the Mesolithic period. No excavations in Europe have turned up such a hint.[ii]
Alexander Marshack concluded that the Ishango bone may actually represent a lunar calendar,[iii] and Claudia Zaslavsky went further to suggest that the creator of the tool was a woman, tracking the lunar phase in relation to the menstrual cycle.[iv] Similar paleolithic era “tally sticks” have been found, including present day Swaziland (the Lebombo bone, dated 37,000 years old and also possibly a lunar calendar[v]) and Czech Republic (the Wolf bone, approximately 30,000 years old[vi]).
Such “calendar sticks” are still used by Bushmen in modern day Namibia. Yet this hasn’t prevented the spread of modern misconceptions about the mathematical abilities of such indigenous people. For example, another indigenous population, the Australian aboriginals, were once thought not to have a way to count beyond two or three.
However, Alfred Howitt, who studied the peoples of southeastern Australia, disproved this in the late nineteenth century, although the myth continues in circulation today. The Australian Aboriginal counting system was used to send messages on message sticks to neighboring clans to alert them of, or invite them to, corroborees, set-fights, and ball games. Numbers could clarify the day the meeting was to be held (in a number of “moons”) and where (the number of camps’ distance away). The messenger would have a verbal message to go along with the message stick.[vii]
Similar forms of enumeration and recording utilized planks of wood, although obviously these would not survive as long as fossilized bone. Also related, but similarly unlikely to survive from a Paleolithic origin are recording systems using knotted cords, a system found among indigenous people throughout the world,[viii] including the ancient Indians of present-day Peru (a system later used by the Inca, who called them quipus, or “talking knots”),[ix] the ancient Persians, and the ancient Chinese. Among the Andaman Islanders, every hunter identifies his arrows and spears by a specific way they tie the cord that secures the tip to the shaft. According to one Chinese text:
In Early Antiquity, knotted cords were used to govern with. Later, our saints replaced them with written characters and tallies. In the ancient past, during the time of Rang Cheng, Xuan Yuan, Fu Xi, and Shen Nong, people tied knots to communicate. For a major matter, use string to tie a big knot; for a minor matter, tie a small knot. The number of knots corresponds to the number of matters to be dealt with.[x]
Both these systems, tally sticks and knotted cords, eventually became widespread in Europe, lasting even after the introduction of modern numerals (again from Original people) made them unnecessary.[xi] In fact, the Catholic rosary is based on the knotted cord system. Yet when colonizing Europeans would later rediscover these intricate systems among Original people, they’d label them primitive.
Binary Prediction Systems
Another system of divination involved the tossing of two-sided objects. In China, this became the I Ching system of divination, which today is done with coins, but was once done with cowry shells. In West Africa, this system occurs as Ifa. Both are binary systems that rely on mathematical laws of probability to “divine” (or predict) possible outcomes in scenarios that have multiple possibilities. Several other indigenous people have also used a binary system involved a two-sided stick.
But such systems aren’t simple. The binary system of I Ching has 64 hexagrams as possible results, each with multiple possible interpretations. In the past, only an adept shaman could reliably explain the results.
This ties us back to the mathematical language of the universe, where gender and polarity are binary indicators of the dual nature of reality itself. By having some way to measure the binary “biases” of a random event, our ancestors sought to see which way the future was headed.
Other cultures used objects with multiple faces. In Volume Two, we’ll talk about the ancient six-sided number cubes found in India, Egypt, and Mesopotamia. Our people have been playing dice for thousands of years. But before dice, binary was all we needed. This way, or that way. And we could make sense of the entire universe from that.
This really turns everything around. It now appears that, yes it seems we didn’t need a whole bunch of written numbers until about 5,000 years ago…yet we somehow had more than enough mathematical understanding over 30,000 years ago. Even the marks on the Ishango bone and Lebombo bone are not the oldest system for mathematical notation. In The Science of Self, we write:
In addition to mathematical artifacts such as those, paleontologists have even found ochre rock art decorated with complex geometric patterns (suggesting we were able to think abstractly older than previously thought) which they date to more than 70,000 years ago in South Africa.[i] Ancient Mesopotamia, Egypt, China, Greece, India, the Incas, the Mayans, and many other cultures have contributed to modern understandings and applications of mathematics.
Can we go back further? We can. We know that the earliest evidence of ANY written symbol goes back to the binary code found in cupules, cave paintings, and other prehistoric art. These dots and lines are no different from the 0s and 1s used to encode even the most advanced computer software, so just consider how deep the meaning of those “primitive” prehistoric symbols could go?
Once we begin reexamining the historical record from the perspective of Original people, who are innately connected to the sciences of the heavens and Earth, we’ll be able to understand these artifacts in a better light. We didn’t need billions of dollars worth of wireless technology, including minerals pillaged from African lands, to send an important message 20,000 years ago. A few lines carved in a bone was enough. Man, can you imagine? Getting back to when we were in our prime like that? Able to read a few dots in a stone and know “Oh damn Labunga’s having a party down on Slauson and Fig Tree, at eight, he says bring all the ladies, it’s gonna be turnt up and we’re having a feast so BYOB.” 20,000 years ago!
Nowadays, we break up over a misunderstood text message. I’m just saying.
 See “The Origins of Religion” and “The Science of Shamanism” in Volume Two.
 For the origin of written numerals, see “The Origin of Numbers” in Volume Two.
 The number of notches on either side of the central column may indicate more than simple counting. The numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the left column are all of the prime numbers between 10 and 20 (which form a prime quadruplet), while those in the right consist of 10+1, 10−1, 20+1 and 20−1. The numbers on each side add up to 60, with the numbers in the central column adding up to 48. Both of these numbers are multiples of 12, suggesting an understanding of multiplication and division.
[i] Brooks, A.S. and Smith, C.C. (1987): “Ishango revisited: new age determinations and cultural interpretations,” The African Archaeological Review, 5: 65-78.
[ii] de Heinzelin, Jean. (June 1962) “Ishango,” Scientific American, 206:6, p. 105-116.
[iii] Marshack, Alexander. (1991). The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
[iv] Zaslavsky, Claudia. (1992) “Women as the First Mathematicians,” International Study Group on Ethnomathematics Newsletter, Volume 7, Number 1.
[v] Peter D. Beaumont. (1973) Border Cave – A Progress Report, S. Afr. J. Science 69.
[vi] Graham Flegg, Numbers: their history and meaning, Courier Dover Publications, 2002
[vii] AW Howitt, (1998) “Notes on Australian Message Sticks and Messengers,” Journal of the Anthropological Institute, pp 317-8, London, 1889, reprinted by Ngarak Press.
[viii] Cyrus L. Day. (Jan 1957). “Knots and Knot Lore: Quipus and Other Mnemonic Knots” Western Folklore, Vol. 16, No. 1, p. 8-26
[ix] Mann, Charles (2005). “Unraveling Khipu’s Secrets.” Science 309: 1008-1009.
[x] Lu, Wei; Aiken, Max. (Nov 2004). “Origins and evolution of Chinese writing systems and preliminary counting relationships” Accounting History.
[xi] Donald Smeltzer. (1958). Man and Number. Emerson Books.